Inference of age‐dependent case‐fatality ratios for seasonal influenza virus subtypes A(H3N2) and A(H1N1)pdm09 and B lineages using data from the Netherlands

Abstract Background Despite the known relatively high disease burden of influenza, data are lacking regarding a critical epidemiological indicator, the case‐fatality ratio. Our objective was to infer age‐group and influenza (sub)type specific values by combining modelled estimates of symptomatic incidence and influenza‐attributable mortality. Methods The setting was the Netherlands, 2011/2012 through 2019/2020 seasons. Sentinel surveillance data from general practitioners and laboratory testing were synthesised to supply age‐group specific estimates of incidence of symptomatic infection, and ecological additive modelling was used to estimate influenza‐attributable deaths. These were combined in an Bayesian inferential framework to estimate case‐fatality ratios for influenza A(H3N2), A(H1N1)pdm09 and influenza B, per 5‐year age‐group. Results Case‐fatality estimates were highest for influenza A(H3N2) followed by influenza B and then A(H1N1)pdm09 and were highest for the 85+ years age‐group, at 4.76% (95% credible interval [CrI]: 4.52–5.01%) for A(H3N2), followed by influenza B at 4.08% (95% CrI: 3.77–4.39%) and A(H1N1)pdm09 at 2.51% (95% CrI: 2.09–2.94%). For 55–59 through 85+ years, the case‐fatality risk was estimated to double with every 3.7 years of age. Conclusions These estimated case‐fatality ratios, per influenza sub(type) and per age‐group, constitute valuable information for public health decision‐making, for assessing the retrospective and prospective value of preventative interventions such as vaccination and for health economic evaluations.


| INTRODUCTION
Seasonal influenza contributes a substantial portion of the global infectious disease mortality burden, especially among older adults. [1][2][3][4] In countries with a temperate climate, influenza is one of the topranked infectious diseases in terms of health burden when measured as disability-adjusted life years (DALY). 5,6 Despite the relatively high disease burden of influenza, data regarding the case-fatality ratio (cfr) following symptomatic infection are scarce. In one of the few studies from which an influenza-attributable cfr can be extracted, 0.19% of a study population of 141,000 influenza patients who consulted their general practitioner (GP) died within 30 days, compared with 0.06% of matched controls. 7 During the recent 2009/2010 influenza A(H1N1)pdm09 pandemic, initiatives to compile surveillance and seroprevalence data of sufficient quality to estimate cfrs per age-group were undertaken, [8][9][10] but comparable figures for influenza A(H1N1)pdm09 in postpandemic years, A(H3N2) and the B lineages are lacking. The reason is that determining both numbers of cases and deaths attributable to influenza is extremely challenging without data sources specifically designed to compile these figures. Influenza A(H3N2) virus infection is suspected to lead to a more severe disease course (including mortality) compared with influenza A(H1N1) virus, 11 with influenza B possibly falling in between, 12 although there is actually little supporting evidence for a consistent difference in clinical severity between influenza A and B. [13][14][15] In the Netherlands, estimates of incidence rates of symptomatic influenza infection are routinely computed using evidence synthesis methods applied to sentinel surveillance of influenza-like illness (ILI), virological testing and other data sources, 16,17 and annual estimates of influenza-attributable mortality are produced from registered cause of death data using established additive regression approaches. 18 Our objective was to combine these two sets of estimates within a statistical modelling framework to infer the cfrs of seasonal influenza per age-group and (sub)type. These case-fatality estimates can be used to improve the accuracy of disease burden calculations. 5

| METHODS
We defined our analysis period to consist of the nine winter seasons   16 and internet survey-based data on health care seeking behaviour, is routinely deployed 16,17 to estimate the incidence rate of symptomatic influenza infection per age-group (defined as <5, 5-14, 15-44, 45-64 and 65+ years; age categories defined based on virological testing data) and per winter season. We multiplied these incidence rates by the 5-year age-group population sizes 20 to obtain season-specific estimates of the number of symptomatic infections per narrow age-group (making the simplifying assumption that ILI rates from sentinel surveillance are applicable to the 5-year agegroups within each broader age-group) ( Figure S4). Furthermore, the laboratory testing of the subset of ILI patients provides quantitative information on the season-specific circulating subtypes/lineages, namely, the proportion of samples per influenza virus A subtype (H3N2, H1N1) and B lineage (Victoria, Yamagata). This allows the ageand season-specific estimates of symptomatic incidence to be further broken down into three categories: influenza A(H3N2), influenza A(H1N1)pdm09 and influenza B (we pool both B lineages due to their relatively small individual contributions over our analysis period).

| Influenza mortality attribution
We adopted an ecological modelling approach frequently used by previous research for attribution of influenza-attributable deaths, 18,[21][22][23] the fundamental assumption of which is that seasonal variability in mortality can be (partly) explained by temporal variation in the reporting incidence of viral or bacterial respiratory disease-causing pathogens.

| Data sources
Attribution of influenza-attributable deaths requires data on the weekly number of deaths from a respiratory cause. Statistics Netherlands registers all deaths in the Netherlands; publicly available weekly all-cause mortality data, stratified into the 'broad' age-groups <65, 65-79 and 80+ years were obtained for our analysis period. 24 Additionally, for the years 2011-2013, we made use of a dataset analysed in our previous study, 25

| Additive regression modelling to infer influenza-attributable deaths
With the use of additive regression modelling, we estimated the weekly number of deaths attributable to influenza after adjusting for the co-circulation of other pathogens and other factors via linear regression techniques. We fitted separate Poisson regression models with an identity link function to allow an additive interpretation of model coefficients, to the weekly respiratory mortality data for each age-group (<55 through 85+ years). As laboratory virological surveillance data were not available stratified by age, each age-group specific additive regression model adjusted for the total reported positive samples per pathogen (i.e., all laboratory weekly surveillance data were used to develop each the regression model for each age-group).
This modelling method is more fully described in previous publications. 18 weather station and available online, 28 and then coding low extreme temperature using the function max(0, 5-T), and high extreme as max(0, T-17), where T is the mean weekly temperature, in degrees Celsius. 18,29 Temperatures as thus treated as 'extreme' if below 5 C or above 17 C.
Next, we conducted a structured model selection procedure separately for each age-group, which involved first entering linear and quadratic trend terms, then testing the impact of 0-to 4-week lags between weekly surveillance reports of influenza A and B viruses and the other co-circulating pathogens and mortality, selecting the lagged pathogen term that led to the largest AIC reduction, then adding terms for low and high extreme temperature terms, and finally adding trigonometric terms to account for the assumed sinusoidal-shaped background mortality (for further details see van Asten et al. and McDonald et al. 18,25 ).
To estimate the number of influenza-attributable deaths among 5-year age-groups below 55-59 years, we used a different approach that was not sensitive to the low counts in these age-groups. For this, we adopted the method implemented in DALY computation software 30 developed for the Burden of Communicable Diseases in Europe (BCoDE) project, 5 which 'redistributes' the total influenzaattributable deaths according to a country-aggregated data source, namely, the observed age-distribution of influenza-coded deaths based on ICD-10 codes, averaged over four countries 2007 only for Italy). We applied the age-group specific proportions from this aggregate data source (among <55 years only) to the total number of estimated deaths in the <55 years age-group for each season, to estimate the number of influenza-attributable deaths per 5-year age-group per season. This aggregate data source indicates a decreasing proportion with decreasing age-group until 5-9 years (see Figure S3); the proportion for 1-4 years is higher than for 5-9 years and higher still for <1 year; this pattern is consistent with clinical data on rates of in-hospital mortality among children hospitalised with confirmed influenza virus infection. 31

| Inference of cfrs for influenza A(H3N2), A(H1N1)pdm09 and influenza B
(Sub)type-aggregated cfrs are calculated by simply dividing the total estimated number of influenza-attributable deaths per age-group by the total estimated number of symptomatic infection cases (i.e., persons with ILI) per age-group. Given that our data (estimated influenza-attributable deaths, derived using additive regression) are not stratified by influenza (sub)type, the task is to find (sub)typedependent cfrs that when multiplied by the (sub)type-specific symptomatic incidence and summed over (sub)type provide a good fit to the observed total number of influenza deaths per season. This is an inferential task, for which a solution can be found using Markov chain Monte-Carlo (MCMC) sampling methods, provided there is sufficient variation in the distribution of circulating type and subtype (within influenza A) over seasons. For example, the presence of multiple seasons with a relatively high proportion of circulating influenza A(H3N2) and multiple seasons with a relatively high proportion of influenza B lineages will help identify these two cfrs.
Because of the relatively low influenza-attributable mortality for age-groups younger than 55 years (see Table 1), we used the inference approach to estimate cfrs for the seven age-groups from 55-59 through 85+ years and a simple extrapolation approach for the younger age-groups (see below). We implemented the below set of equations in JAGS 32 and took 8000 samples from the posterior distributions for age-specific cfrs after discarding 15,000 iterations as 'burn-in'. Note that as computation is carried out within a Bayesian framework, taking the 2.5% and 97.5% quantiles of the posterior distribution yields 95% credible intervals (CrIs). While the 95% intervals for (sub)type-aggregated cfrs were estimated by propagating the uncertainty in influenza-attributable mortality and symptomatic incidence in JAGS, uncertainty in the parameters incidence, mortality and (sub)type-positive proportions could not be supplied as prior distributions in the inferential model. This is because the 'best-fitting solution' (i.e., converged-upon posterior distribution) may also adjust, sometimes drastically, of the posterior distributions for three parameters, which results in the inference of unrealistic cfrs.
We model the observed data, Z a,i , as the summation of the (unknown) (sub)type-specific influenza deaths (i.e., Y H3N2,a,i + Y H1N1,a, i + Y B,a,i ) using the sum sampler in JAGS ( Figure S5 provides a directed acyclic graph of the statistical model). We use the index i to refer to the season of the analysis period, the index a to refer to the 5-year age-group and the index s to refer to the (sub)type. Y s,a,i is therefore the number of respiratory deaths in season i and age-group a among persons infected with influenza (sub)type s.
The unknown number of (sub)type-specific influenza deaths is assumed to follow a Poisson distribution: The Poisson rate parameter, λ s,a,i , is a function of the (sub)typeand age-dependent cfr (cfr) and the constants: the proportion of each (sub)type circulating per season (π s,i ) and the estimated symptomatic The cfr is defined in turn to be a multiplicative function of a (sub) type-specific cfr and age; we therefore define log (cfr) to be an additive function of a (sub)type-specific constant term (β s ) and the ageeffect coefficient (μ) multiplied by the reference age (in years; we define the reference age [age.ref] as the lower bound of the agegroup minus 50). This enforces an identical exponential relationship between cfr and (absolute) age for each (sub)type; this relationship is illustrated in a plot of the type-aggregated data ( Figure S1, ages 55-59 and older): Given the Bayesian framework, prior distributions are required for stochastic parameters. Therefore, we assign vague normal priors to β s and μ, where the precision (1/sd 2 ) = 0.001 β s $ Normal 0, sd 2 : μ $ Normal 0, sd 2 : Finally, extrapolation of (sub)type-specific cfrs downwards to the age-groups 50-54 years and younger was conducted by multiplying the cfr estimated for 55-59 years by the separate age-effects for 50-54 through 10-14 years and for 5-9 years through <1 year, which were separately estimated via log-linear regression analysis of the type-aggregated data ( Figure S1).   (Table 1), which was consistently observed across seasons (Figure 1).

| RESULTS
The re-distribution of the total respiratory deaths and total modelled influenza-attributable deaths for the <55 years among the 12 younger age-groups is provided in  Figure 2). The cfr was 2-3 orders of magnitude times smaller for the 55-59 years age-group (0.018%, 0.016% and 0.010%, for A(H3N2), B and A(H1N1)pdm09, respectively).
Extrapolated cfrs for the age-groups 50-54 years and below are shown in Figure 2.
The predicted number of influenza deaths per (sub)type and season (i.e., the quantity estimated using Equation 2) is shown in Model validity can be ascertained by comparing the total predicted influenza deaths (computed using the inferred cfrs) with the regression-modelled influenza-attributable deaths, per season and age-group ( Figure S2)   because the method takes advantage of variation in the (sub)type distribution across seasons and is not sensitive to absolute proportions.
Nevertheless, because the inferred cfrs for influenza B are based on the aggregated data, a potential difference in severity between the two lineages cannot be recovered. As B/Yagamata has not been detected since April 2020 and appears to be extinct, 38 the generalisability of our influenza B case-fatality estimates to future seasons with appreciable circulation of B/Victoria is unknown.
We highlight the following limitations of our analysis. The inferred cfrs are sensitive to season-specific vaccine effectiveness (VE)seasonal variation in VE due to strain variability and vaccine (mis) match 26 -which, although the model provided real-world case-fatality estimates for our analysis period, these may not generalise to future situations with improved vaccines. As such, some portion of the between-(sub)type difference we observed may be attributable to these factors. The age effect on cfrs was constrained to be identical for the three (sub)types, when in reality, ratios could reflect an interaction between (sub)type and age-group. This is because mortality risk is influenced by both vaccine match and VE (for age-groups with high vaccine uptake) and by pre-existing immunity, for instance if a particular (sub)type circulated widely within the same age-group or within age-groups that have high contact rates with this age-group, in the prior season(s). Related to this point, we estimated cfrs for age-groups below 55-59 years using an extrapolation approach based on piecewise age-effects and (sub)type-specific cfrs derived from analysis of the 55-59 through 85+ years age-groups. This was necessitated by the low number of influenza-attributable deaths per season estimated for younger persons, which could not be fitted in the current framework.
Although influenza-attributable deaths were reasonably wellpredicted for seven of the nine seasons, we observed discrepancies for several age-groups for 2011/2012 and 2012/2013; we note that in 2011/2012, the total estimated symptomatic incident cases were very low ( Figure S4) compared with the total influenza-attributable deaths (Figure 1), which underlies the lower model-predicted values.
Such discrepancies are due to factors associated with variation in inci-  40 ), which suggests that underestimation was minimal.
The data sources underlying our symptomatic incidence estimates are from the general, non-institutionalised population, but mortality data are from the entire population, which could lead to overestimation of the cfrs for institutional residents with a higher underlying mortality rate. However, given that only about 10% of persons aged 65+ years live in nursing or elderly homes, 41 the impact on influenza incidence and consequently on case-fatality estimates is expected to be small for all but the oldest age-groups.
In summary, we estimated age-specific cfrs for A(H3N2), A(H1N1)pdm09 and influenza B in a Bayesian inferential modelling framework. These cfrs can be used to estimate influenzaattributable mortality in comparable settings for which data on